Many existing structures suffer from damage due to age or accumulated damage from hazards. It is important to accurately assess the present conditions of these aging, deteriorating, and damaged structures. In recent years, laser scanners have been increasingly used for capturing the in situ conditions of structures. They are used for collecting dense and high-resolution point clouds of scenes for structural engineering applications. However, automatically extracting meaningful information from the point clouds remains a challenge, and the current state-of-the-art requires significant user interaction. In this work, a process for automatically extracting information from laser datasets such as the location, orientation, and size of objects in a scanned region, and location of damaged regions on a structure is established. First, widely accepted point cloud processing steps are used to divide the collected laser scanner data into meaningful point clusters. A new graph-based object detection algorithm is then used to generate skeletons of the extracted point clusters in order to detect structural members by using a model library consisting of common structural shapes. The obtained member information is then used for developing a new graph-based damage detection method, which compares the fitted object model with the as-is point cloud of the investigated object for locating defects, detecting alignment issues and points of discontinuity, computing changes in the cross-section through area calculation, and determining the total volume change on the investigated member. The effectiveness of the developed graph-based object and damage detection algorithms are tested and validated on test specimens and test-bed bridges.